Classical algebra is a generalization of arithmetic in which symbols are utilized for unknown numbers. The principles of classical algebra were synthesized in the 9th Century A.D. from earlier understandings by Abu Jafar Muhammad ibn Musa Al-Khwarizm. Algebra spread subsequently from Northwest Africa to what is now Spain, from Spain throughout Europe, and from Europe to substantially the entire world.
Algebra and its derivatives are mathematical languages which are now almost universally utilized to explain and understand the philosophies underlying science and engineering. While there are notable exceptions, engineers and scientists, whether those scientists are physical scientists or social scientists, quantify the phenomena with which they are concerned so as to provide some common ground allegedly understood by at least those who appreciate the language of mathematics. In the modern world, a person may have a magnificent mechanical aptitude or an innate understanding of economics, politics, and sociology; but, without an understanding and appreciation of algebra, massive quantities of information are simply unavailable to that person. Worse still for everyone, that person is quite likely to be ignored.
In order to widen the participation of people in a modern society, it is necessary for as many people as possible to have an understanding and appreciation of quantitative concepts. After a person has acquired some facility with arithmetic, the next level is algebra. Algebra is used as a vehicle to understand not only chemistry, physics, engineering and economics, but also music, biology, sociology and even politics. In politics, for example, a voter who is interested in the election of only one candidate, and who has some familiarity with algebra, can more readily appreciate that on a ballot having five candidates on which the voter is allowed to vote for three, only one vote should be cast, since a vote for the two other candidates might diminish the chances of that voter's candidate prevailing. A child who might aspire to being a chemist, physician, engineer or corporate executive, has his or her chances severely comprised if that child does not understand algebra, since without an understanding of algebra, it is highly unusual for a student to succeed in trigonometry or calculus. In our society, algebra is a gate which must be opened in order to understand the language in which many other concepts are taught; and it is generally agreed that the more people who traverse the algebraic gate, the more knowledgeable a society, in general, becomes.
It is believed by many who have studied the subject that current methods of teaching algebra to children, as well as to adults, are counter-intuitive and defy common sense. Accordingly, many people are of the opinion that it is not in their best interest to learn algebra even though in the general scheme of things, people who understand algebra, or who have understood algebra, appear as a group to be better off than those who do not understand algebra. For the most part, it appears that those who do understand algebra would like to keep it that way, which is only natural. Some think that restricting access to such knowledge is counter-productive and would like as many people as possible to understand the language of algebra. They have undertaken activities such as the ALGEBRA PROJECT.TM. in order to include as many people as possible in the circle of those who understand and appreciate algebra.
In teaching algebra, a difficulty appears to arise when a student attempts to make the transition from arithmetic to algebra. To facilitate this transition, a discipline known as "pre-algebra" has arisen. It is the opinion of some people that pre-algebra is more difficult to teach and progress in than actual algebra because pre-algebra requires an understanding of numbers which is not readily apparent from the exercises that one undertakes to understand and appreciate arithmetic. Accordingly, there is a need for vehicles that convey these understandings and thereafter smoothly merge these understandings with classical algebra while providing insight into more sophisticated concepts.